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<link title="Weak" rel="Chapter" href="Weak.html"><title>Complex</title>
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<h1>Module <a href="type_Complex.html">Complex</a></h1>
<pre><span id="MODULEComplex"><span class="keyword">module</span> Complex</span>: <code class="code"><span class="keyword">sig</span></code> <a href="Complex.html">..</a> <code class="code"><span class="keyword">end</span></code></pre><div class="info module top">
<div class="info-desc">
<p>Complex numbers.</p>
<p>This module provides arithmetic operations on complex numbers.
Complex numbers are represented by their real and imaginary parts
(cartesian representation). Each part is represented by a
double-precision floating-point number (type <code class="code">float</code>).</p>
</div>
</div>
<hr width="100%">
<pre><code><span id="TYPEt"><span class="keyword">type</span> <code class="type"></code>t</span> = {</code></pre><table class="typetable">
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTt.re">re</span> : <code class="type">float</code>;</code></td>
</tr>
<tr>
<td align="left" valign="top" >
<code> </code></td>
<td align="left" valign="top" >
<code><span id="TYPEELTt.im">im</span> : <code class="type">float</code>;</code></td>
</tr></table>
}
<div class="info ">
<div class="info-desc">
<p>The type of complex numbers. <code class="code">re</code> is the real part and <code class="code">im</code> the
imaginary part.</p>
</div>
</div>
<pre><span id="VALzero"><span class="keyword">val</span> zero</span> : <code class="type"><a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>The complex number <code class="code">0</code>.</p>
</div>
</div>
<pre><span id="VALone"><span class="keyword">val</span> one</span> : <code class="type"><a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>The complex number <code class="code">1</code>.</p>
</div>
</div>
<pre><span id="VALi"><span class="keyword">val</span> i</span> : <code class="type"><a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>The complex number <code class="code">i</code>.</p>
</div>
</div>
<pre><span id="VALneg"><span class="keyword">val</span> neg</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Unary negation.</p>
</div>
</div>
<pre><span id="VALconj"><span class="keyword">val</span> conj</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Conjugate: given the complex <code class="code">x + i.y</code>, returns <code class="code">x - i.y</code>.</p>
</div>
</div>
<pre><span id="VALadd"><span class="keyword">val</span> add</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Addition</p>
</div>
</div>
<pre><span id="VALsub"><span class="keyword">val</span> sub</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Subtraction</p>
</div>
</div>
<pre><span id="VALmul"><span class="keyword">val</span> mul</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Multiplication</p>
</div>
</div>
<pre><span id="VALinv"><span class="keyword">val</span> inv</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Multiplicative inverse (<code class="code">1/z</code>).</p>
</div>
</div>
<pre><span id="VALdiv"><span class="keyword">val</span> div</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Division</p>
</div>
</div>
<pre><span id="VALsqrt"><span class="keyword">val</span> sqrt</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Square root. The result <code class="code">x + i.y</code> is such that <code class="code">x > 0</code> or
<code class="code">x = 0</code> and <code class="code">y >= 0</code>.
This function has a discontinuity along the negative real axis.</p>
</div>
</div>
<pre><span id="VALnorm2"><span class="keyword">val</span> norm2</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Norm squared: given <code class="code">x + i.y</code>, returns <code class="code">x^2 + y^2</code>.</p>
</div>
</div>
<pre><span id="VALnorm"><span class="keyword">val</span> norm</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Norm: given <code class="code">x + i.y</code>, returns <code class="code">sqrt(x^2 + y^2)</code>.</p>
</div>
</div>
<pre><span id="VALarg"><span class="keyword">val</span> arg</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> float</code></pre><div class="info ">
<div class="info-desc">
<p>Argument. The argument of a complex number is the angle
in the complex plane between the positive real axis and a line
passing through zero and the number. This angle ranges from
<code class="code">-pi</code> to <code class="code">pi</code>. This function has a discontinuity along the
negative real axis.</p>
</div>
</div>
<pre><span id="VALpolar"><span class="keyword">val</span> polar</span> : <code class="type">float -> float -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p><code class="code">polar norm arg</code> returns the complex having norm <code class="code">norm</code>
and argument <code class="code">arg</code>.</p>
</div>
</div>
<pre><span id="VALexp"><span class="keyword">val</span> exp</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Exponentiation. <code class="code">exp z</code> returns <code class="code">e</code> to the <code class="code">z</code> power.</p>
</div>
</div>
<pre><span id="VALlog"><span class="keyword">val</span> log</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Natural logarithm (in base <code class="code">e</code>).</p>
</div>
</div>
<pre><span id="VALpow"><span class="keyword">val</span> pow</span> : <code class="type"><a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a> -> <a href="Complex.html#TYPEt">t</a></code></pre><div class="info ">
<div class="info-desc">
<p>Power function. <code class="code">pow z1 z2</code> returns <code class="code">z1</code> to the <code class="code">z2</code> power.</p>
</div>
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